Scientists answer questions;
e.g. "is there life on Mars?"
Engineers solve problems;
e.g. "Plan the most fuel efficient trajectory to place an instrument package on the north pole of mars."
To which his supervisor may add "and have the
details of the plan on my desk by this afternoon."
Don Schulz

I remember a similar story:
A trash can in the office is on fire. A Mathematician stops by and after writing some equations declares: "The solution exists". A Physicist stops by and after some calculations declares: "The solution is feasible". An Engineer shows up, gets a bucket of water and puts the fire out!

A scientist, an engineer and a mathematician are sharing a hotel room, when in the middle of the night they awaken to discover that the TV set is on fire.
The scientist grabs a pencil and paper and begins calculating the precise quantity of water required to put out the fire and the flow rate required to obtain that quantity of water from the bathroom faucet.
The mathematician grabs a pencil and paper and begins deriving a proof that it is possible to put out the fire.
The engineer grabs an empty trash can, runs to the bathroom and fills it with water, then dumps it onto the TV set, extinguishing the fire.

Here is a quote from an unforgotten Engineer: "A scientist might be called a person who can show something working once. An engineer must figure out how to make products that will last considerably longer than the warranty period." (Bob Pease, Electronic Design 21.11.94)

MIT professor Steve Senturia is credited with the following definition:
"Engineering is the purposeful use of science"
If I could only come up with an equally good definition of 'science', we'd be done.